Sub-diffraction limit image resolution in three dimensions

ABSTRACT

The present invention generally relates to sub-diffraction limit image resolution and other imaging techniques, including imaging in three dimensions. In one aspect, the invention is directed to determining and/or imaging light from two or more entities separated by a distance less than the diffraction limit of the incident light. For example, the entities may be separated by a distance of less than about 1000 nm, or less than about 300 nm for visible light. In some cases, the position of the entities can be determined in all three spatial dimensions (i.e., in the x, y, and z directions), and in certain cases, the positions in all three dimensions can be determined to an accuracy of less than about 1000 nm. In one set of embodiments, the entities may be selectively activatable, i.e., one entity can be activated to produce light, without activating other entities. A first entity may be activated and determined (e.g., by determining light emitted by the entity), then a second entity may be activated and determined. The emitted light may be used to determine the x and y positions of the first and second entities, for example, by determining the positions of the images of these entities, and in some cases, with sub-diffraction limit resolution. In some cases, the z positions may be determined using one of a variety of techniques that uses intensity information or focal information (e.g., a lack of focus) to determine the z position. Non-limiting examples of such techniques include astigmatism imaging, off-focus imaging, or multi-focal-plane imaging. Other aspects of the invention relate to systems for sub-diffraction limit image resolution, computer programs and techniques for sub-diffraction limit image resolution, methods for promoting sub-diffraction limit image resolution, and the like.

RELATED APPLICATIONS

This application is a continuation of U.S. Ser. No. 15/623,658, filedJun. 15, 2017, entitled “Sub-Diffraction Limit Image Resolution in ThreeDimensions,” by Zhuang, et al., which is a continuation of U.S. Ser. No.14/821,569, filed Aug. 7, 2015, entitled “Sub-Diffraction Limit ImageResolution in Three Dimensions,” by Zhuang, et al., which is acontinuation of U.S. Ser. No. 14/022,168, filed Sep. 9, 2013, entitled“Sub-Diffraction Limit Image Resolution in Three Dimensions,” by Zhuang,et al., which is a continuation of U.S. Ser. No. 13/899,215, filed May21, 2013, entitled “Sub-Diffraction Limit Image Resolution in ThreeDimensions,” by Zhuang, et al., which is a continuation of U.S. Ser. No.12/746,784, filed Jun. 8, 2010, entitled “Sub-Diffraction Limit ImageResolution in Three Dimensions,” by Zhuang, et al., which is a U.S.National Application of PCT/US2008/013915, filed Dec. 19, 2008, entitled“Sub-Diffraction Limit Image Resolution in Three Dimensions,” by Zhuang,et al., which claims the benefit of U.S. Provisional Patent ApplicationSer. No. 61/008,661, filed Dec. 21, 2007, entitled “Sub-DiffractionLimit Image Resolution in Three Dimensions,” by Zhuang, et al., eachincorporated herein by reference.

GOVERNMENT FUNDING

This invention was made with government support under Grant. No.GM068518 awarded by the National Institutes of Health. The U.S.Government has certain rights in the invention.

FIELD OF INVENTION

The present invention generally relates to sub-diffraction limit imageresolution and other imaging techniques, including imaging in threedimensions.

BACKGROUND

Fluorescence microscopy is widely used in molecular and cell biology andother applications for non-invasive, time-resolved imaging. Despitethese advantages, standard fluorescence microscopy is not useful forultra-structural imaging, due to a resolution limit set by thediffraction of light. Several approaches have been employed to try topass this diffraction limit, including near-field scanning opticalmicroscopy (NSOM), stimulated emission depletion (STED), reversiblesaturable optical linear fluorescence transition (RESOLFT), andsaturated structured-illumination microscopy (SSIM), but each hascertain unsatisfactory limitations. Electron microscopy is often usedfor high resolution imaging of biological samples, but electronmicroscopy uses electrons, rather than light, and is difficult to usewith biological samples due to its preparation requirements.Accordingly, new techniques, including non-invasive techniques areneeded to harness the benefits of fluorescence microscopy, forultra-resolution imaging of biological and other samples, e.g., to allowmolecular specificity and/or compatibility with live biological samples.

SUMMARY OF THE INVENTION

The present invention generally relates to sub-diffraction limit imageresolution and other imaging techniques, including imaging in threedimensions. The subject matter of the present invention involves, insome cases, interrelated products, alternative solutions to a particularproblem, and/or a plurality of different uses of one or more systemsand/or articles.

In one aspect, the invention is directed to a method. In one set ofembodiments, the method includes acts of providing a first entity and asecond entity separated by a distance of less than about 1000 nm,determining light emitted by the first entity, determining light emittedby the second entity, and determining x, y, and z positions of the firstentity and the second entity using the light emitted by the first entityand the light emitted by the second entity. The method, in another setof embodiments, includes acts of providing a first entity and a secondentity separated by a distance of separation, determining light emittedby the first entity, determining light emitted by the second entity, anddetermining x, y, and z positions of the first entity and the secondentity using the light emitted by the first entity and the light emittedby the second entity.

According to yet another set of embodiments, the method includes acts ofproviding a first entity and a second entity separated by a distance ofless than about 1000 nm, activating the first entity but not the secondentity, determining light emitted by the first entity, activating thesecond entity, determining light emitted by the second entity, anddetermining x, y, and z positions of the first entity and the secondentity using the light emitted by the first entity and the light emittedby the second entity. In still another set of embodiments, the methodincludes acts of providing a first entity and a second entity separatedby a distance of separation, activating the first entity but not thesecond entity, determining light emitted by the first entity, activatingthe second entity, determining light emitted by the second entity, anddetermining x, y, and z positions of the first entity and the secondentity using the light emitted by the first entity and the light emittedby the second entity.

In one set of embodiments, the method includes acts of providing aplurality of entities able to emit light (at least some of which areseparated by a distance of less than about 1000 nm), activating afraction of the plurality of entities to emit light, determining theemitted light, deactivating the activated fraction of the plurality ofentities, and repeating the acts of activating and deactivating theplurality of entities to determine x, y, and z positions of theplurality of entities. The method, in yet another set of embodiments,includes acts of providing a plurality of entities able to emit light,activating a fraction of the plurality of entities to emit light,determining the emitted light, deactivating the activated fraction ofthe plurality of entities, and repeating the acts of activating anddeactivating the plurality of entities to determine x, y, and zpositions of the plurality of entities.

In another aspect, the present invention is directed to a method ofmaking one or more of the embodiments described herein. In anotheraspect, the present invention is directed to a method of using one ormore of the embodiments described herein.

Other advantages and novel features of the present invention will becomeapparent from the following detailed description of various non-limitingembodiments of the invention when considered in conjunction with theaccompanying figures. In cases where the present specification and adocument incorporated by reference include conflicting and/orinconsistent disclosure, the present specification shall control. If twoor more documents incorporated by reference include conflicting and/orinconsistent disclosure with respect to each other, then the documenthaving the later effective date shall control.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the present invention will be described byway of example with reference to the accompanying figures, which areschematic and are not intended to be drawn to scale. In the figures,each identical or nearly identical component illustrated is typicallyrepresented by a single numeral. For purposes of clarity, not everycomponent is labeled in every figure, nor is every component of eachembodiment of the invention shown where illustration is not necessary toallow those of ordinary skill in the art to understand the invention. Inthe figures:

FIGS. 1A-1G illustrate one embodiment of the invention, useful fordetermining the position of an entity in three dimensions;

FIGS. 2A-2F illustrates another embodiment of the invention, useful forimaging cells;

FIGS. 3A-3H illustrate three-dimensional imaging of a cell, according toanother embodiment of the invention;

FIGS. 4A-4D illustrate three-dimensional imaging of various beads, inaccordance with one embodiment of the invention;

FIGS. 5A-5C illustrate the accuracy of imaging a cell, according to oneembodiment of the invention; and

FIGS. 6A-6E illustrate various fluorescent compounds useful in certainembodiments of the invention.

DETAILED DESCRIPTION

The present invention generally relates to sub-diffraction limit imageresolution and other imaging techniques, including imaging in threedimensions. In one aspect, the invention is directed to determiningand/or imaging light from two or more entities separated by a distanceless than the diffraction limit of the incident light. For example, theentities may be separated by a distance of less than about 1000 nm, orless than about 300 nm for visible light. In some cases, the position ofthe entities can be determined in all three spatial dimensions (i.e., inthe x, y, and z directions), and in certain cases, the positions in allthree dimensions can be determined to an accuracy of less than about1000 nm. In one set of embodiments, the entities may be selectivelyactivatable, i.e., one entity can be activated to produce light, withoutactivating other entities. A first entity may be activated anddetermined (e.g., by determining light emitted by the entity), then asecond entity may be activated and determined. The emitted light may beused to determine the x and y positions of the first and secondentities, for example, by determining the positions of the images ofthese entities, and in some cases, with sub-diffraction limitresolution. In some cases, the z positions may be determined using oneof a variety of techniques that uses intensity information or focalinformation (e.g., a lack of focus) to determine the z position.Non-limiting examples of such techniques include astigmatism imaging,off-focus imaging, or multi-focal-plane imaging. Other aspects of theinvention relate to systems for sub-diffraction limit image resolution,computer programs and techniques for sub-diffraction limit imageresolution, methods for promoting sub-diffraction limit imageresolution, and the like.

One aspect of the invention is generally directed to techniques forresolving two or more entities, even at distances of separation that areless than the wavelength of the light emitted by the entities or belowthe diffraction limit of the emitted light. The resolution of theentities may be, for instance, on the order of 1 micrometer (1000 nm) orless, as described herein. For example, if the emitted light is visiblelight, the resolution may be less than about 700 nm. In some cases, two(or more) entities may be resolved even if separated by a distance ofless than about 500 nm, less than about 300 nm, less than about 200 nm,less than about 100 nm, less than about 80 nm, less than about 60 nm,less than about 50 nm, or less than about 40 nm. In some cases, two ormore entities separated by a distance of less than about 20 nm or lessthan 10 nm can be resolved using embodiments of the present invention.

The entities may be any entity able to emit light. For instance, theentity may be a single molecule. Non-limiting examples of emissiveentities include fluorescent entities (fluorophores) or phosphorescententities, for example, cyanine dyes (e.g., Cy2, Cy3, Cy5, Cy5.5, Cy7,etc.) metal nanoparticles, semiconductor nanoparticles or “quantumdots,” or fluorescent proteins such as GFP (Green Fluorescent Protein).Other light-emissive entities are readily known to those of ordinaryskill in the art. As used herein, the term “light” generally refers toelectromagnetic radiation, having any suitable wavelength (orequivalently, frequency). For instance, in some embodiments, the lightmay include wavelengths in the optical or visual range (for example,having a wavelength of between about 400 nm and about 1000 nm, i.e.,“visible light”), infrared wavelengths (for example, having a wavelengthof between about 300 micrometers and 700 nm), ultraviolet wavelengths(for example, having a wavelength of between about 400 nm and about 10nm), or the like. In certain cases, as discussed in detail below, morethan one entity may be used, i.e., entities that are chemicallydifferent or distinct, for example, structurally. However, in othercases, the entities may be chemically identical or at leastsubstantially chemically identical.

In some cases, one or more of the entities is “switchable,” i.e., theentity can be switched between two or more states, at least one of whichemits light having a desired wavelength. In the other state(s), theentity may emit no light, or emit light at a different wavelength. Forinstance, an entity may be “activated” to a first state able to producelight having a desired wavelength, and “deactivated” to a second state.In some cases, at least one of these entities are photoactivatable orphotoswitchable. An entity is “photoactivatable” if it can be activatedby incident light of a suitable wavelength. An entity is“photoswitchable” if it can be switched between different light-emittingor non-emitting states by incident light of different wavelengths.Typically, a “switchable” entity can be identified by one of ordinaryskill in the art by determining conditions under which an entity in afirst state can emit light when exposed to an excitation wavelength,switching the entity from the first state to the second state, e.g.,upon exposure to light of a switching wavelength, then showing that theentity, while in the second state can no longer emit light (or emitslight at a reduced intensity) or emits light at a different wavelengthwhen exposed to the excitation wavelength. Examples of switchableentities are discussed in detail below, and are also discussed inInternational Patent Application No. PCT/US2007/017618, filed Aug. 7,2007, entitled “Sub-Diffraction Limit Image Resolution and Other ImagingTechniques,” published as Int. Pat. Apl. Pub. No. WO 2008/091296 on Jul.31, 2008, incorporated herein by reference.

In some aspects, the light may be processed to determine the spatialpositions of the two or more entities. In some cases, the positions ofone or more entities, distributed within an image, may each beindividually determined, and in some cases, the positions of theentities may be determined in 3 dimensions (i.e., in the x, y, and zdimensions, where the z dimension is the direction of the optical axisof the imaging system and the x and y dimensions are perpendicular tothe z direction, and to each other). In one set of embodiments, theemitted light may be processed, using Gaussian fitting or other suitabletechniques, to localize the position of each of the emissive entities.Details of one suitable Gaussian fit technique are described in theExamples, below; those of ordinary skill in the art will be able toidentify other suitable image-processing techniques with the benefit ofthe present disclosure.

Another example of an image-processing technique follows, in accordancewith another embodiment of the invention. Starting with a series ofimages of a sample (e.g., a movie), each light-emission peak (e.g.,through fluorescence, phosphorescence, etc.) is identified, and thetimes which the peak is present are determined. For example, a peak maybe present with approximately the same intensity in a series of imageswith respect to time. Peaks may be fit, in some cases, to Gaussianand/or elliptical Gaussian functions to determine their centroidpositions, intensities, widths, and/or ellipticities. Based on theseparameters, peaks which are too dim, too wide, too skewed, etc. to yieldsatisfactory localization accuracy may be rejected in certain cases fromfurther analysis. Peaks which are sporadic, moving, discontinuouslypresent, etc. may also be discarded. By determining the center positionof the peak, for example, using least-squares fitting to a 2-dimensionalGaussian function of the peak intensities, the location of the source ofthe peak (e.g., any entity or entities able to emit light, as discussedherein) can be determined. This process may be repeated as necessary forany or all of the peaks within the sample.

In one set of embodiments, the z position of an entity can be determinedat a resolution that is less than the diffraction limit of the incidentlight. For example, for visible light, the z position of an entity canbe determined at a resolution less than about 800 nm, less than about500 nm, less than about 200 nm, less than about 100 nm, less than about50 nm, less than about 20 nm, or less than about 10 nm. Any microscopytechnique able to determine the z position of entity may be used, forinstance, astigmatism imaging, off-focus imaging, multi-focal planeimaging, confocal microscopy, two-photon microscopy, or the like. Insome cases, the entity may be positioned and imaged such that the entitydoes not appear as a single point of light, but as an image that hassome area, for example, as a slightly unresolved or unfocused image. Asan example, the entity may be imaged by a lens or a detector system thatdefines one or more focal regions (e.g., one or more focal planes) thatdo not contain the entity, such that the image of the entity at thedetector appears unfocused. The degree to which the entity appearsunfocused can be used to determine the distance between the entity andone of the focal regions, which can then be used to determine the zposition of the entity.

In one embodiment, the z position can be determined using astigmatismimaging. A lens may be used that is not circularly symmetric withrespect to the direction light emitted by the entity passes through thelens. For instance, the lens may be cylindrical (as is shown in FIG.1A), ellipsoidal, or the like. In some cases, the lens may havedifferent radii of curvature in different planes. The light emitted bythe entity after passing through the imaging optical system whichincludes this non-circularly symmetric lens may appear circular orelliptical at the detector.

The size and ellipticity of the image can be used, in some cases, todetermine the distance between the entity and the focal region of thelens or the detector, which can then be used to determine the zposition. As a non-limiting example, as shown in FIG. 1B, an image infocus (z=0 nm) appears circular, while images that are out of focusappear increasingly elliptical (z=±200 nm or ±400 nm), with thedirection of ellipticity indicating whether the entity is above or belowthe focal region.

In another embodiment, the z position can be determined using off-focusimaging. An entity not in one of the focal regions defined by a lens ora detector system used to image the entity may appear to be unfocused,and the degree that the image appears unfocused may be used to determinethe distance between the entity and the focal region of the lens, whichcan then be used to determine the z position. In some cases, the imageof the unfocused entity may appear generally circular (with the areabeing indicative of the distance between the entity and the focal regionof the lens), and in some instances, the image of the unfocused entitymay appear as a series of ring-like structures, with more ringsindicating greater distance).

In some embodiments, e.g., with multi-focal plane imaging, the lightemitted by the entities may be collected by a plurality of detectors. Insome cases, at one or more of the detectors, the light may appear to beunfocused. The degree that the images appear unfocused may be used todetermine the z position.

In another non-limiting example of a suitable imaging processingtechnique of the present invention, a series of images of a sample (e.g.a movie) may include a repetitive sequence of activation frames (e.g.,in which the activation light is on) and imaging frames (e.g., in whichthe imaging light is on). For one or more of the imaging frames,fluorescent peaks on each frame can be determined to determine theirpositions, intensities, widths, ellipticities, etc. Based on theseparameters, peaks that are too dim, too wide, too skewed, etc. to yieldsatisfactory localization accuracy may be rejected from furtheranalysis. Peaks which are sporadic, moving, discontinuously present,etc. may also be discarded in some cases. By determining the centerposition, the shape, and/or the size of the peak, the location of thesource of the peak (e.g., any entity or entities able to emit light, asdiscussed herein) can be determined. In some cases, the position may bedetermined in 3 dimensions. This process may also be repeated asnecessary for any or all of the peaks within the sample.

Other image-processing techniques may also be used to facilitatedetermination of the entities, for example, drift correction or noisefilters may be used. Generally, in drift correction, for example, afixed point is identified (for instance, as a fiduciary marker, e.g., afluorescent particle may be immobilized to a substrate), and movementsof the fixed point (i.e., due to mechanical drift) are used to correctthe determined positions of the switchable entities. In another examplemethod for drift correction, the correlation function between imagesacquired in different imaging frames or activation frames can becalculated and used for drift correction. In some embodiments, the driftmay be less than about 1000 nm/min, less than about 500 nm/min, lessthan about 300 nm/min, less than about 100 nm/min, less than about 50nm/min, less than about 30 nm/min, less than about 20 nm/min, less thanabout 10 nm/min, or less than 5 nm/min. Such drift may be achieved, forexample, in a microscope having a translation stage mounted for x-ypositioning of the sample slide with respect to the microscopeobjective. The slide may be immobilized with respect to the translationstage using a suitable restraining mechanism, for example, spring loadedclips. In addition, a buffer layer may be mounted between the stage andthe microscope slide. The buffer layer may further restrain drift of theslide with respect to the translation stage, for example, by preventingslippage of the slide in some fashion. The buffer layer, in oneembodiment, is a rubber or polymeric film, for instance, a siliconerubber film. Accordingly, one embodiment of the invention is directed toa device, comprising a translation stage, a restraining mechanism (e.g.,a spring loaded clip) attached to the translation stage able toimmobilize a slide, and optionally, a buffer layer (e.g., a siliconerubber film) positioned such that a slide restrained by the restrainingmechanism contacts the buffer layer. To stabilize the microscope focusduring data acquisition, a “focus lock” device may be used in somecases. As a non-limiting example, to achieve focus lock, a laser beammay be reflected from the substrate holding the sample and the reflectedlight may be directed onto a position-sensitive detector, for example, aquadrant photodiode. In some cases, the position of the reflected laser,which may be sensitive to the distance between the substrate and theobjective, may be fed back to a z-positioning stage, for example apiezoelectric stage, to correct for focus drift.

In one set of embodiments, as discussed, a switchable entity may beused. Non-limiting examples of switchable entities are discussed inInternational Patent Application No. PCT/US2007/017618, filed Aug. 7,2007, entitled “Sub-Diffraction Limit Image Resolution and Other ImagingTechniques,” published as Int. Pat. Apl. Pub. No. WO 2008/091296 on Jul.31, 2008, incorporated herein by reference. As a non-limiting example ofa switchable entity, Cy5 can be switched between a fluorescent and adark state in a controlled and reversible manner by light of differentwavelengths, e.g., 633 nm or 657 nm red light can switch or deactivateCy5 to a stable dark state, while 532 nm green light can switch oractivate the Cy5 back to the fluorescent state. Other non-limitingexamples of a switchable entity including photoactivatable orphotoswitchable fluorescent proteins, or photoactivatable orphotoswitchable inorganic particles, e.g., as discussed herein. In somecases, the entity can be reversibly switched between the two or morestates, e.g., upon exposure to the proper stimuli. For example, a firststimuli (e.g., a first wavelength of light) may be used to activate theswitchable entity, while a second stimuli (e.g., a second wavelength oflight) may be used to deactivate the switchable entity, for instance, toa non-emitting state. Any suitable method may be used to activate theentity. For example, in one embodiment, incident light of a suitablewavelength may be used to activate the entity to emit light, i.e., theentity is photoswitchable. Thus, the photoswitchable entity can beswitched between different light-emitting or non-emitting states byincident light, e.g., of different wavelengths. The light may bemonochromatic (e.g., produced using a laser) or polychromatic. Inanother embodiment, the entity may be activated upon stimulation byelectric field and/or magnetic field. In other embodiments, the entitymay be activated upon exposure to a suitable chemical environment, e.g.,by adjusting the pH, or inducing a reversible chemical reactioninvolving the entity, etc. Similarly, any suitable method may be used todeactivate the entity, and the methods of activating and deactivatingthe entity need not be the same. For instance, the entity may bedeactivated upon exposure to incident light of a suitable wavelength, orthe entity may be deactivated by waiting a sufficient time.

In some embodiments, the switchable entity includes a first,light-emitting portion (e.g., a fluorophore), and a second portion thatactivates or “switches” the first portion. For example, upon exposure tolight, the second portion of the switchable entity may activate thefirst portion, causing the first portion to emit light. Examples ofactivator portions include, but are not limited to, Alexa Fluor 405(Invitrogen), Alexa 488 (Invitrogen), Cy2 (GE Healthcare), Cy3 (GEHealthcare), Cy3.5 (GE Healthcare), or Cy5 (GE Healthcare), or othersuitable dyes. Examples of light-emitting portions include, but are notlimited to, Cy5, Cy5.5 (GE Healthcare), or Cy7 (GE Healthcare), AlexaFluor 647 (Invitrogen), or other suitable dyes. These may linkedtogether, e.g., covalently, for example, directly, or through a linker,e.g., forming compounds such as, but not limited to, Cy5-Alexa Fluor405, Cy5-Alexa Fluor 488, Cy5-Cy2, Cy5-Cy3, Cy5-Cy3.5, Cy5.5-Alexa Fluor405, Cy5.5-Alexa Fluor 488, Cy5.5-Cy2, Cy5.5-Cy3, Cy5.5-Cy3.5, Cy7-AlexaFluor 405, Cy7-Alexa Fluor 488, Cy7-Cy2, Cy7-Cy3, Cy7-Cy3.5, or Cy7-Cy5.The structures of Cy3, Cy5, Cy5.5, and Cy 7 are shown in FIG. 6 with anon-limiting example of a linked version of Cy3-Cy5 shown in FIG. 6E;those of ordinary skill in the art will be aware of the structures ofthese and other compounds, many of which are available commercially.

Any suitable method may be used to link the first, light-emittingportion and the second, activation portion. In some cases, a linker ischosen such that the distance between the first and second portions issufficiently close to allow the activator portion to activate thelight-emitting portion as desired, e.g., whenever the light-emittingportion has been deactivated in some fashion. Typically, the portionswill be separated by distances on the order of 500 nm or less, forexample, less than about 300 nm, less than about 100 nm, less than about50 nm, less than about 20 nm, less than about 10 nm, less than about 5nm, less than about 2 nm, less than about 1 nm, etc. Examples of linkersinclude, but are not limited to, carbon chains (e.g., alkanes oralkenes), polymer units, or the like.

In certain cases, the light-emitting portion and the activator portions,when isolated from each other, may each be fluorophores, i.e., entitiesthat can emit light of a certain, emission wavelength when exposed to astimulus, for example, an excitation wavelength. However, when aswitchable entity is formed that comprises the first fluorophore and thesecond fluorophore, the first fluorophore forms a first, light-emittingportion and the second fluorophore forms an activator portion thatswitches that activates or “switches” the first portion in response to astimulus. For example, the switichable entity may comprise a firstfluorophore directly bonded to the second fluorophore, or the first andsecond entity may be connected via a linker or a common entity. Whethera pair of light-emitting portion and activator portion produces asuitable switchable entity can be tested by methods known to those ofordinary skills in the art. For example, light of various wavelength canbe used to stimulate the pair and emission light from the light-emittingportion can be measured to determined wither the pair makes a suitableswitch.

Accordingly, in one embodiment of the invention, a light-emittingswitchable entity is provided, comprising a first, light emittingportion and a second, activation portion. The entity has a maximumemission wavelength determined by the first, light emitting portion anda maximum activation wavelength determined by the second, activationportion. Notably, the two wavelengths are not controlled by the samemolecular entity, and are effectively decoupled. In some cases, the samewavelength light can be used both for activating the emitting portion toa fluorescent state and for exciting emission from and deactivating theemitting portion. Further, multiple types of switchable entities withina sample may be independently determined. For example, two switchableentities having the same activator portions but different light-emissionportions can be activated by the same wavelength light applied to thesample, but emit at different wavelengths due to differentlight-emission portions and can be easily distinguished, even atseparation distances of less than sub-diffraction limit resolutions.This can effectively yield two colors in the image. Similarly, twoswitchable entities having the same light-emission portions butdifferent activator portions can be activated by different wavelengthlight applied to the sample, due to the different activator portions,and the light-emission portions may emit at same wavelengths and canthus be distinguished, even at separation distances of less thansub-diffraction limit resolutions. This also can effectively yield twocolors in the image. When these methods are combined, four (or more)color images can be readily produced. Using this principle, multi-colorimaging can be scaled up to 6 colors, 9 colors, etc., depending on theswitchable and/or activator entities. This multi-color imaging principlemay also be used with the imaging methods described herein to yieldsub-diffraction limit resolutions (in all three dimensions in somecases), and/or used to obtained multi-color images with other imagingmethods not limited to sub-diffraction limit resolutions.

In some embodiments, the first, light-emitting portion and the second,activation portion as described above may not be directly covalentlybonded or linked via a linker, but are each immobilized relative to acommon entity. In other embodiments, two or more of the switchableentities (some of which can include, in certain cases, a first,light-emitting portion and a second, activation portion linked togetherdirectly or through a linker) may be immobilized relative to a commonentity in some aspects of the invention. The common entity in any ofthese embodiments may be any nonbiological entity or biological entity,for example, a cell, a tissue, a substrate, a surface, a polymer, abiological molecule such as a nucleic acid (DNA, RNA, PNA, LNA, or thelike), a lipid molecule, a protein or a polypeptide, or the like, abiomolecular complex, or a biological structure, for example, anorganelle, a microtubule, a clathrin-coated pit, etc.

In one set of embodiments, the switchable entity can be immobilized,e.g., covalently, with respect to a binding partner, i.e., a moleculethat can undergo binding with a particular analyte. Binding partnersinclude specific, semi-specific, and non-specific binding partners asknown to those of ordinary skill in the art. The term “specificallybinds,” when referring to a binding partner (e.g., protein, nucleicacid, antibody, etc.), refers to a reaction that is determinative of thepresence and/or identity of one or other member of the binding pair in amixture of heterogeneous molecules (e.g., proteins and other biologics).Thus, for example, in the case of a receptor/ligand binding pair, theligand would specifically and/or preferentially select its receptor froma complex mixture of molecules, or vice versa. Other examples include,but are not limited to, an enzyme would specifically bind to itssubstrate, a nucleic acid would specifically bind to its complement, anantibody would specifically bind to its antigen. The binding may be byone or more of a variety of mechanisms including, but not limited toionic interactions, and/or covalent interactions, and/or hydrophobicinteractions, and/or van der Waals interactions, etc. By immobilizing aswitchable entity with respect to the binding partner of a targetmolecule or structure (e.g., DNA or a protein within a cell), theswitchable entity can be used for various determination or imagingpurposes. For example, a switchable entity having an amine-reactivegroup may be reacted with a binding partner comprising amines, forexample, antibodies, proteins or enzymes.

In some embodiments, more than one switchable entity may be used, andthe entities may be the same or different. In some cases, the lightemitted by a first entity and the light emitted by a second entity havethe same wavelength. The entities may be activated at different timesand the light from each entity may be determined separately. This allowsthe location of the two entities to be determined separately and, insome cases, the two entities may be spatially resolved, as discussed indetail below, even at distances of separation that are less than thewavelength of the light emitted by the entities or below the diffractionlimit of the emitted light (i.e., “sub-diffraction limit” resolutions).In certain instances, the light emitted by a first entity and the lightemitted by a second entity have different wavelengths (for example, ifthe first entity and the second entity are chemically different, and/orare located in different environments). The entities may be spatiallyresolved even at distances of separation that are less than thewavelength of the light emitted by the entities or below the diffractionlimit of the emitted light. In certain instances, the light emitted by afirst entity and the light emitted by a second entity have substantiallythe same wavelengths, but the two entities may be activated by light ofdifferent wavelengths and the light from each entity may be determinedseparately. The entities may be spatially resolved even at distances ofseparation that are less than the wavelength of the light emitted by theentities, or below the diffraction limit of the emitted light.

In some cases, the entities may be independently switchable, i.e., thefirst entity may be activated to emit light without activating a secondentity. For example, if the entities are different, the methods ofactivating each of the first and second entities may be different (e.g.,the entities may each be activated using incident light of differentwavelengths). As another non-limiting example, if the entities aresubstantially the same, a sufficiently weak intensity may be applied tothe entities such that only a subset or fraction of the entities withinthe incident light are activated, i.e., on a stochastic or random basis.Specific intensities for activation can be determined by those ofordinary skill in the art using no more than routine skill. Byappropriately choosing the intensity of the incident light, the firstentity may be activated without activating the second entity. As anothernon-limiting example, the sample to be imaged may comprise a pluralityof entities, some of which are substantially identical and some of whichare substantially different. In this case, one or more of the abovemethods may be applied to independently switch the entities.

Light emitted by each of the entities may be determined, e.g., as animage or matrix. For example, the first entity may be activated and thelight emitted by the first entity determined, and the second entity maybe activated (with or without deactivating the first entity) and lightemitted by the second entity may be determined. The light emitted byeach of the plurality of entities may be at the same or differentwavelengths. Any suitable method may be used to determine the emittedlight. For instance, a detector of the light may be, for instance, acamera such as a CCD camera, a photodiode, a photodiode array, aphotomultiplier, a photomultiplier array, a spectrometer, or the like;those of ordinary skill in the art will know of other suitabletechniques. In some cases, more than one detector may be used, and thedetectors may each independently be the same or different. In somecases, multiple images (or other determinations) may be used, forexample, to improve resolution and/or to reduce noise. For example, atleast 2, at least 5, at least 10, at least 20, at least 25, at least 50,at least 75, at least 100, etc. images may be determined, depending onthe application.

In some cases, incident light having a sufficiently weak intensity maybe applied to a plurality of entities such that only a subset orfraction of the entities within the incident light are activated, e.g.,on a stochastic or random basis. The amount of activation may be anysuitable fraction, e.g., about 0.1%, about 0.3%, about 0.5%, about 1%,about 3%, about 5%, about 10%, about 15%, about 20%, about 25%, about30%, about 35%, about 40%, about 45%, about 50%, about 55%, about 60%,about 65%, about 70%, about 75%, about 80%, about 85%, about 90%, orabout 95% of the entities may be activated, depending on theapplication. For example, by appropriately choosing the intensity of theincident light, a sparse subset of the entities may be activated suchthat at least some of them are optically resolvable from each other andtheir positions can be determined. In some embodiments, the activationof the subset of the entities can be synchronized by applying a shortduration of the incident light. Iterative activation cycles may allowthe positions of all of the entities, or a substantial fraction of theentities, to be determined. In some cases, an image with sub-diffractionlimit resolution can be constructed using this information.

Multiple locations on a sample may each be analyzed to determine theentities within those locations. For example, a sample may contain aplurality of various entities, some of which are at distances ofseparation that are less than the wavelength of the light emitted by theentities or below the diffraction limit of the emitted light. Differentlocations within the sample may be determined (e.g., as different pixelswithin an image), and each of those locations independently analyzed todetermine the entity or entities present within those locations. In somecases, the entities within each location may be determined toresolutions that are less than the wavelength of the light emitted bythe entities or below the diffraction limit of the emitted light, aspreviously discussed.

In some embodiments of the invention, the entities may also be resolvedas a function of time. For example, two or more entities may be observedat various time points to determine a time-varying process, for example,a chemical reaction, cell behavior, binding of a protein or enzyme, etc.Thus, in one embodiment, the positions of two or more entities may bedetermined at a first point of time (e.g., as described herein), and atany number of subsequent points of time. As a specific example, if twoor more entities are immobilized relative to a common entity, the commonentity may then be determined as a function of time, for example,time-varying processes such as movement of the common entity, structuraland/or configurational changes of the common entity, reactions involvingthe common entity, or the like. The time-resolved imaging may befacilitated in some cases since a switchable entity can be switched formultiple cycles, each cycle give one data point of the position of theentity.

Another aspect of the invention is directed to a computer-implementedmethod. For instance, a computer and/or an automated system may beprovided that is able to automatically and/or repetitively perform anyof the methods described herein. As used herein, “automated” devicesrefer to devices that are able to operate without human direction, i.e.,an automated device can perform a function during a period of time afterany human has finished taking any action to promote the function, e.g.by entering instructions into a computer. Typically, automated equipmentcan perform repetitive functions after this point in time. Theprocessing steps may also be recorded onto a machine-readable medium insome cases.

Still another aspect of the invention is generally directed to a systemable to perform one or more of the embodiments described herein. Forexample, the system may include a microscope, a device for activatingand/or switching the entities to produce light having a desiredwavelength (e.g., a laser or other light source), a device fordetermining the light emitted by the entities (e.g., a camera, which mayinclude color-filtering devices, such as optical filters), and acomputer for determining the spatial positions of the two or moreentities. In some cases, mirrors (such as dichroic mirror or apolychroic mirror), prisms, lens, diffraction gratings, or the like maybe positioned to direct light from the light source. In some cases, thelight sources may be time-modulated (e.g., by shutters, acoustic opticalmodulators, or the like). Thus, the light source may be one that isactivatable and deactivatable in a programmed or a periodic fashion. Inone embodiment, more than one light source may be used, e.g., which maybe used to illuminate a sample with different wavelengths or colors. Forinstance, the light sources may emanate light at different frequencies,and/or color-filtering devices, such as optical filters or the like maybe used to modify light coming from the light sources such thatdifferent wavelengths or colors illuminate a sample.

In some embodiments, a microscope may be configured so to collect lightemitted by the switchable entities while minimizing light from othersources of fluorescence (e.g., “background noise”). In certain cases,imaging geometry such as, but not limited to, atotal-internal-reflection geometry a spinning-disc confocal geometry, ascanning confocal geometry, an epi-fluorescence geometry, etc., may beused for sample excitation. In some embodiments, a thin layer or planeof the sample is exposed to excitation light, which may reduceexcitation of fluorescence outside of the sample plane. A high numericalaperture lens may be used to gather the light emitted by the sample. Thelight may be processed, for example, using filters to remove excitationlight, resulting in the collection of emission light from the sample. Insome cases, the magnification factor at which the image is collected canbe optimized, for example, when the edge length of each pixel of theimage corresponds to the length of a standard deviation of a diffractionlimited spot in the image.

In some cases, a computer may be used to control excitation of theswitchable entities and the acquisition of images of the switchableentities. In one set of embodiments, a sample may be excited using lighthaving various wavelengths and/or intensities, and the sequence of thewavelengths of light used to excite the sample may be correlated, usinga computer, to the images acquired of the sample containing theswitchable entities. For instance, the computer may apply light havingvarious wavelengths and/or intensities to a sample to yield differentaverage numbers of activated switchable elements in each region ofinterest (e.g., one activated entity per location, two activatedentities per location, etc). In some cases, this information may be usedto construct an image of the switchable entities, in some cases atsub-diffraction limit resolutions, as noted above.

In other aspects of the invention, the systems and methods describedherein may also be combined with other imaging techniques known to thoseof ordinary skill in the art, such as high-resolution fluorescence insitu hybridization (FISH) or immunofluorescence imaging, live cellimaging, confocal imaging, epi-fluorescence imaging, total internalreflection fluorescence imaging, etc.

The following documents are incorporated herein by reference: U.S.patent application Ser. No. 12/012,524, filed Feb. 1, 2008, entitled“Sub-Diffraction Image Resolution and other Imaging Techniques,”published as U.S. Pat. Apl. Pub. No. 2008/0182336 on Jul. 31, 2008;International Patent Application No. PCT/US2007/017618, filed Aug. 7,2007, entitled “Sub-Diffraction Limit Image Resolution and Other ImagingTechniques,” published as Int. Pat. Apl. Pub. No. WO 2008/091296 on Jul.31, 2008; U.S. patent application Ser. No. 11/605,842, filed Nov. 29,2006, entitled “Sub-Diffraction Image Resolution and other ImagingTechniques,” published as U.S. Pat. Apl. Pub. No. 2008/0032414 on Feb.7, 2008; U.S. Provisional Patent Application Ser. No. 60/836,167, filedAug. 7, 2006, entitled “Sub-Diffraction Image Resolution”; U.S.Provisional Patent Application Ser. No. 60/836,170, filed Aug. 8, 2006,entitled “Sub-Diffraction Image Resolution”; and U.S. Provisional PatentApplication Ser. No. 61/008,661, filed Dec. 21, 2007, entitled“Sub-Diffraction Limit Image Resolution in Three Dimensions.”

The following examples are intended to illustrate certain embodiments ofthe present invention, but do not exemplify the full scope of theinvention.

Example 1

This example demonstrates 3-dimensional imaging with a spatialresolution that is about 10 times better than the diffraction limit inall three dimensions without invoking sample or optical beam scanning.In International Patent Application No. PCT/US2007/017618, filed Aug. 7,2007, entitled “Sub-Diffraction Limit Image Resolution and Other ImagingTechniques,” published as Int. Pat. Apl. Pub. No. WO 2008/091296 on Jul.31, 2008, incorporated herein by reference, the photo-switchable natureof certain fluorophores was used to separate the otherwise spatiallyoverlapping images of numerous molecules, and high degrees oflocalization were achieved in the lateral dimensions for individualfluorescent dyes.

However, this example, and the following examples, illustrates imagingin all three dimensions by stochastic activation of an opticallyresolvable subset of photoswitchable probes, determination of thecoordinates for each probe with high accuracy, and construction of athree-dimensional high-resolution image through multiple activationcycles. In some cases, while the lateral position of a particle (orother suitable object) can be determined from the centroid of its image,the shape of the image may also contain information about the particle'saxial or z position.

This example uses astigmatism imaging to achieve three-dimensionalimaging, although other techniques including but not limited tooff-focus imaging, multi-focal plane imaging, and the like, could beused in other cases. To this end, a weak cylindrical lens was introducedinto the imaging path to create two slightly different focal planes forthe x and y directions (FIG. 1A). This figure shows thethree-dimensional localization of individual fluorophores. Thesimplified optical diagram illustrates the principle of determining thez-coordinate of a fluorescent object from the ellipticity of its imageby introducing a cylindrical lens into the imaging path. The right panelshows the images of a fluorophore at various z positions.

As a result, the ellipticity and orientation of a fluorophore's imagevaried as its position changed in z: when the fluorophore was in theaverage focal plane (approximately half-way between the x and y focalplanes, where the point-spread-function (PSF) has essentially equalwidths in the x and y directions), the image appeared round; when thefluorophore was above the average focal plane, its image was morefocused in the y direction than in the x direction and thus appearedellipsoidal with its long axis along x; conversely when the fluorophorewas below the focal plane, the image appeared ellipsoidal with its longaxis along y. By fitting the image with a two-dimensional ellipticalGaussian function, the x and y coordinates of the peak position could beobtained, as well as the peak widths w_(x) and w_(y), which in turnallowed the z coordinate of the fluorophore to be determined.

To experimentally generate a calibration curve of w_(x) and w_(y) as afunction of z, Alexa 647-labeled streptavidin molecules were immobilizedon a glass surface and individual molecules were imaged to determine thew_(x) and w_(y) values as the sample was scanned in z (FIG. 1C). FIG. 1Cis the calibration curve of the image widths w_(x) and w_(y) as afunction of z obtained from single Alexa 647 molecules in this example.Each data point represents the average value obtained from 6 molecules.The data were fit to a defocusing function (red curve) as describedbelow.

In this image analysis, the z coordinate of each photoactivatedfluorophore was determined by comparing the measured w_(x) and w_(y)values of its image with the calibration curves. In addition, forsamples immersed in aqueous solution on a glass substrate, all zlocalizations were rescaled by a factor of 0.79 to account for therefractive index mismatch between glass and water (see below foradditional details).

In some cases, the three-dimensional resolution of the techniques inthis example were limited by the accuracy with which individualphotoswitchable fluorophores could be localized in all three dimensionsduring a switching cycle. International Patent Application No.PCT/US2007/017618, filed Aug. 7, 2007, entitled “Sub-Diffraction LimitImage Resolution and Other Imaging Techniques,” published as Int. Pat.Apl. Pub. No. WO 2008/091296 on Jul. 31, 2008, incorporated herein byreference, discloses a family of photo-switchable cyanine dyes (Cy5,Cy5.5, Cy7 and Alexa Fluor 647) that can be reversibly cycled between afluorescent and a dark state by light of different wavelengths. Thereactivation efficiency of these photo-switchable “reporters” dependscritically on the proximity of an “activator” dye, which can be any oneof a variety of dye molecules (e.g. Cy3, Cy2, Alexa Fluor 405). In thisparticular example, Cy3 and Alexa 647 were used as the activator andreporter pair to perform imaging. A red laser (657 nm) was used to imageAlexa 647 molecules and deactivate them to the dark state, whereas agreen laser (532 nm) was used to reactivate the fluorophores. Eachactivator-reporter pair could be cycled on and off hundreds of timesbefore permanent photobleaching occurred, and an average of 6000 photonswere detected per switching cycle using objective-typetotal-internal-reflection fluorescence (TIRF) or epi-fluorescenceimaging geometry. This reversible switching behavior provides aninternal control to measure the localization accuracy.

In some experiments, streptavidin molecules doubly labeled with Cy3 andAlexa 647 were immobilized on a glass surface. The molecules were thenswitched on and off for multiple cycles, and their x, y, and zcoordinates were determined for each switching cycle. This procedureresulted in a cluster of localizations for each molecule (FIG. 1D). Inthis figure, each molecule gives a cluster of localizations due torepetitive activation of the same molecule. Localizations from 145clusters were aligned to their center-of-mass to generate the overall 3Dpresentation of the localization distribution (left panel). Histogramsof the distribution in x, y and z (right panels) were fit to a Gaussianfunction, yielding the standard deviation of 9 nm in x, 11 nm in y, and22 nm in z. The standard deviation (SD: 9 nm in x, 11 nm in y, and 22 nmin z) or full-width-half-maximum (FWHM: 21 nm in x, 26 nm in y, and 52nm in z) of the localization distribution provided a quantitativemeasure of localization accuracy in 3 dimensions (FIG. 1E-1G). Thelocalization accuracies in the two lateral dimensions were similar toprevious resolutions obtained without the cylindrical lens. Thelocalization accuracy in z was approximately twice those in x and y inthese experiments. Because the image width increased as the fluorophoremoves away from the focal plane, the localization accuracy decreasedwith increasing z values, especially in the lateral dimensions. Thus, insome experiments, a, z imaging depth of about 600 nm near the focalplane was chosen, within which the lateral and axial localizationaccuracies changed by less than 1.6 fold and 1.3 fold, respectively, incomparison with the values obtained at the average focal plane. Theimaging depth may, however, be increased, e.g., by employing z scanningin future experiments.

As an initial test, a model bead sample was imaged. The model beadsample was prepared by immobilizing 200 nm biotinylated polystyrenebeads on a glass surface and then incubating the sample with Cy3-Alexa647 labeled streptavidin to coat the beads with photoswitchable probes.Three-dimensional images of the beads were obtained by iterative,stochastic activation of sparse subsets of optically resolvable Alexa647 molecules, allowing the x, y and z coordinates of individualmolecules to be determined. Over the course of multiple activationcycles, the positions of numerous fluorophores were determined and usedto construct a full three-dimensional image. The projections of the beadimages appeared approximately spherical when viewed along all threedirections with average diameters of 210±16, 225±25 and 228±25 nm in x,y and z respectively (FIG. 4), indicating accurate localization in allthree dimensions. As the image of each fluorophore simultaneouslyencodes its x, y and z coordinates, no additional time was required tolocalize each molecule in three-dimensions as compared withthree-dimensional imaging.

FIG. 4 shows three-dimensional images of 200 nm diameter beads coatedwith Cy3-Alexa 647 labeled streptavidin. FIG. 4A shows the x-zprojection of two beads within an area of 1.7 micrometers (x)×10micrometers (y) on the glass surface. The surface is defined by a lineof localizations underneath the beads, resulting from streptavidinmolecules nonspecifically adsorbed to the glass surface. Although thenon-specifically adsorbed streptavidins were only sparsely distributedon the surface, a large area projection results in an almost continuousline of localizations. The inset in FIG. 4A shows the x-z projection ofa small volume (400 nm×400 nm×400 nm) surrounding the right bead, wherea few non-specifically adsorbed streptavidin molecules were present.FIGS. 4B and 4C show the x-y projection of the two beads. The slightdeviation from a round shape may be in part due to the imperfectstreptavidin coating and/or the intrinsically non-ideal bead shape.

FIG. 4D illustrates the distribution of the bead diameters in the x, yand z directions. To determine the diameters in a non-subjective manner,the streptavidin molecules were assumed to be coated uniformly on thebead surface. Such a 3D uniform distribution on a spherical surface,when projected onto any of the x, y and z axes, should follow a 1Duniform distribution. The width of the 1D distribution in the x, y or zdirections provides a measure of the diameter of the bead along the x, yor z axis, respectively. In addition, the mathematical relation betweenthe width (d) and the standard deviation (SD_(uniform)) of a uniformdistribution can be used in some cases, i.e. SD_(uniform) ²=d²/12 andthe relation between the measured standard deviation SD_(measure) andthe SD_(uniform) of the true uniform distribution considering finitelocalization accuracy (SD_(localization)), i.e. SD_(measure)²=SD_(uniform) ²+SD_(localization) ². From the independently measuredlocalization accuracies as shown in FIGS. 1E-1F, and the SD_(measure) ofthe projected distribution of the 3D bead image in the x, y and zdirections, the diameters (d) of the beads were deduced along the x, yand z axes. The diameter distributions of 53 measured beads are shownhere and the average diameters are 210±16 nm, 226±25 nm, and 228±25 nmin the x, y and z directions, respectively. The measured diameters arequantitatively similar to the manufacturer's suggested diameter (200 nm)for the beads. The slight increase may be in part due to the finitethickness of the streptavidin coating.

Cell imaging is described as another example. In this example, indirectimmunofluorescence imaging was performed of the microtubule network ingreen monkey kidney epithelial (BS-C-1) cells. Cells were immunostainedwith primary antibodies and then with Cy3 and Alexa 647 doubly-labeledsecondary antibodies. The three-dimensional images that were obtainednot only showed a substantial improvement in the resolution as comparedto the conventional wide-field fluorescence image (FIGS. 2A-2B), butalso provided z-dimension information (FIG. 2B) that was not availablein the conventional image (FIG. 2A). FIG. 2A is a conventional indirectimmunofluorescence image of microtubules in a large area of a BS-C-1cell; FIG. 2B is of the same area, imaging using the techniquesdescribed herein and shaded according to z-position information.Multiple layers of microtubule filaments were clearly visible in thex-y, x-z or y-z cross sections of the cell (FIGS. 2C-2E). This region isthe region outlined by the white box in FIG. 2B, showing 5 microtubulefilaments.

To characterize the cell imaging resolution more quantitatively,point-like objects were identified in the cell that appeared as smallclusters of localizations away from any discernable microtubulefilaments. These clusters may represent individual antibodiesnonspecifically attached to the cell. The FWHM of these clusters, whichwere randomly chosen over the entire measured z-range of the cell, were22 nm in x, 28 nm in y and 55 nm in z (FIG. 5), quantitatively similarto those determined for individual molecules immobilized on a glasssurface (compare FIG. 5 with FIG. 1E-1G). Two microtubule filamentsseparated by 102 nm in z appeared well separated in thethree-dimensional image (FIG. 2F), which shows the z profile of twomicrotubules crossing in the x-y projection. This histogram shows thedistribution of z-coordinates of the localizations, fit to a doubleGaussian with identical width (curve). The apparent width of themicrotubule filaments in the z dimension was 66 nm, slightly larger thanthe intrinsic imaging resolution in z, and quantitatively agreeing withthe convolution of the imaging resolution and the independently measuredwidth of antibody-coated microtubule (FIG. 2F). As the effectiveresolution was determined by a combination of the intrinsic imagingresolution and the size of the labels (such as the antibodies),improvement in the resolution may be achieved by using direct instead ofindirect immunofluorescence to remove one layer of antibody labeling, asshown in the next example, or by using Fab fragments or geneticallyencoded peptide tags to replace antibodies.

In FIG. 5, the localization accuracy was determined from point-likeobjects in a cell, which appeared as small clusters of localizationsaway from any discernable microtubule filaments. Shown here are thespatial distribution of localizations within these point-like clustersin the x, y and z dimensions. The histogram of localizations wasgenerated by aligning 202 clusters by their centers of mass, with eachcluster containing ≥8 localizations. Fitting the histograms withGaussian functions gives standard deviations of 9 nm, 12 nm, and 23 nmin the x, y and z directions, respectively. The corresponding FWHMvalues were 22 nm, 28 nm and 55 nm.

Finally, to demonstrate that the three-dimensional morphology ofnanoscopic structures in cells could be resolved, clathrin-coated pits(CCP) were imaged in BS-C-1 cells. CCPs are 150 nm to 200 nm sphericalcage-like structures assembled from clathrin, adaptor proteins and othercofactors on the cytoplasmic side of the cell membrane to facilitateendocytosis. To image CCPs, a direct immunofluorescence scheme was used,using the Cy3 and Alexa 647 doubly-labeled primary antibodies forclathrin. When imaged by conventional fluorescence microscopy, all CCPsappeared as nearly diffraction-limited spots with no discernablestructure (FIG. 3A, which is a conventional direct immunofluorescenceimage of a region of a BS-C-1 cell). In two-dimensional images using thetechniques described herein in which the z-dimension information wasdiscarded, the round shape of CCPs was observable (FIGS. 3B and 3D). Thesize distribution of CCPs measured from the 2D projection image, 180±40nm, agrees quantitatively with the size distribution determined usingelectron microscopy. Including the z-dimension information allows thevisualization of the 3D structure of the pits (FIGS. 3C and 3E-3H).FIGS. 3C and 3E show the x-y cross-sections of the image, taken from aregion near the opening of the pits at the cell surface. FIG. 3C is a 50nm thick x-y cross-section of the same area as shown in FIGS. 3A-3B,showing the ring-like structure of the opening of the CCPs at the plasmamembrane, while FIG. 3E is a magnified view of the 100 nm thick x-ycross-section of two nearby CCPs.

The circular ring-like structure of the pit periphery was unambiguouslyresolved. The consecutive x-y and x-z cross-sections of the pits (FIGS.3F-3H) revealed the three-dimensional half-spherical-cage likemorphology of these nanoscopic structures that was not observable in thetwo-dimensional images. These figures show x-y cross-sections (each 50nm thick in z) (FIG. 3F) and the serial x-z cross-sections (each 50 nmthick in y) (FIG. 3G) of a CCP, and an x-y and x-z cross sectionpresented in 3D perspective (FIG. 3H), showing the half-spherical-cagelike structure of the pit.

In summary, these examples illustrate three-dimensional, high-resolutionimaging with resolutions on the order of 100 nm or less. Nanoscalefeatures of cellular structures were resolved at a resolution previouslyonly seen with electron microscopy, and now optically with molecularspecificity under ambient conditions. This development may significantlyenhance the ability to visualize molecular organization and interactionnetworks in cells.

Example 2

This example describes certain techniques useful with respect toExample 1. To characterize the 3D localization accuracy of thephotoswitchable probes of Example 1, streptavidin molecules (Invitrogen)were labeled with photoswitchable Alexa 647 fluorophore (Invitrogen) andthe activator dye Cy3 (GE Healthcare) by incubating the protein withamine-reactive dyes following the suggested protocol from themanufacturers. Unreacted dye molecules were removed by gel filtrationusing a Nap-5 column (GE Healthcare). The labeling ratio wascharacterized by a UV-Vis spectrophotometer, and the absorption spectrumindicated a labeling ratio of ˜2 Cy3 and ˜0.1 Alexa 647 per streptavidinmolecule. The labeled streptavidin was then immobilized onto the surfaceof a glass flow chamber assembled from a glass slide and a #1.5coverglass. Slides and coverglasses were cleaned by sonicating in 1 Mpotassium hydroxide for 15 min, followed by extensive washing withMilliQ water and drying with compressed nitrogen. The labeledstreptavidin sample was injected into the flow chamber to allow thestreptavidin to adsorb directly on the surface non-specifically orthrough a biotin-streptavidin linkage on the biotinylated bovine serumalbumin (BSA) coated surface. To generate the calibration curve for zlocalization measurement, Alexa 647-labeled streptavidin or quantum dots(Protein A coated Qdot 655, Invitrogen) were also used. The singlylabeled streptavidin were immobilized to the chamber surfaces in asimilar manner as the Cy3 and Alexa 647 doubly-labeled streptavidin andthe quantum dots were immobilized directly to the surface by nonspecificbinding.

To make 200 nm polystyrene beads coated with photoswitchablefluorophores, the coverglass surface was first coated with streptavidinby flowing 0.25 mg/mL unlabeled streptavidin solution into the flowchamber as described above and then rinsed with phosphate bufferedsaline (PBS). Next, 200 nm diameter biotinylated polystyrene beads(Invitrogen) were added to the chamber to allow immobilization on thesurface. Finally 3 micrograms/mL Cy3 and Alexa 647 doubly streptavidinlabeled was flowed in to coat the surface of the biotinlylated beads.During this procedure, some fluorescent streptavidin also adsorbednon-specifically onto the coverglass surface. The flow chamber was thenrinsed with PBS to remove free streptavidin molecules in solution.

BS-C-1 cells were plated in 8-well chambered coverglasses (LabTek-II,Nalgene Nunc) at a density of 40 k cells per well. After 16 to 24 hours,the cells were fixed using 3% paraformaldehyde and 0.1% glutaraldehydein PBS for 10 min, and then treated with 0.1% sodium borohydride for 7min to reduce the unreacted aldehyde groups and fluorescent productsformed during fixation. The sodium borohydride solution was preparedimmediately before use to avoid hydrolysis. The fixed sample was thenwashed three times with PBS, and permeabilized in blocking buffer (3%w/v BSA, 0.5% v/v Triton X-100 in PBS) for 15 min.

Microtubules were stained with mouse monoclonal β-tubulin antibodies(ATN01, Cytoskeleton) for 30 min and then goat anti-mouse secondaryantibodies for 30 min. The secondary antibodies were labeled withamine-reactive Alexa 647 and Cy3 and the labeling stoichiometry wascharacterized to be ˜4.0 Cy3 and ˜0.4 Alexa 647 per antibody on average.Three washing steps using 0.2% w/v BSA and 0.1% v/v Triton-X100 in PBSwere performed after each staining step.

For staining clathrin by direct immunofluorescence, mouse monoclonalanti-clathrin heavy chain (clone X22, ab2731, Abcam) and anti-clathrinlight chain (clone CON.1, C1985, Sigma-Aldrich) were usedsimultaneously. Both antibodies were labeled with ˜1.0 Cy3 and ˜1.0Alexa 647 per antibody. The sample was stained for 30 min, washed threetimes with PBS and used immediately for imaging.

It should be noted that the immunofluorescence imaging can work well ata wide range of dye-labeling ratios. Typically a labeling ratio of ≥1activator (Cy3 in this case) per antibody was chosen to ensure that themajority of antibodies had activators. On the other hand, when more thanone photo-switchable reporter (Alexa 647 in this case) were attached toamino acid residues within close proximity on the same antibody, thereporter-reporter interaction can result in a significantly lower rateof switching off in some cases. Previous characterizations haveindicated that the off rate of two reporters separated by 2 nm was ˜5times slower than that of a single reporter whereas the two reportersseparated by 7 nm have comparable off rate as that of an isolatedreporter. Therefore, a dye/protein ratio of ≤1 was chosen for thereporter to minimize this effect.

Buffer solutions in the samples were replaced with an imaging bufferimmediately before data acquisition. The imaging buffer contained 50 mMTris, pH 7.5, 10 mM NaCl, 0.5 mg/mL glucose oxidase (G2133,Sigma-Aldrich), 40 micrograms/mL catalase (106810, Roche AppliedScience), 10% (w/v) glucose and 1% (v/v) beta-mercaptoethanol. It wasfound that beta-mercaptoethanol (or other thiol-containing reagents suchas cysteine) were important for photoswitching of the cyanine dyes.Imaging may also be performed at lower beta-mercaptoethanolconcentrations (e.g. 0.1% v/v), which are compatible with live cellimaging. In this work, all of the imaging experiments described abovewere performed on fixed cells.

All of the imaging experiments described in Example 1 were performed onan inverted optical microscope (Olympus IX-71). Two solid state laserswere used as the excitation source: a 657 nm laser (RCL-200-656,Crystalaser) for exciting the photo-switchable reporter fluorophore(Alexa 647) and switching it to the dark state; and a 532 nm laser(GCL-200-L, Crystalaser) for reactivating the Alexa 647 in aCy3-facilitated manner. The two laser beams were combined and coupledinto an optical fiber (P3-630A-FC-5, Thorlabs). The fiber output wascollimated and focused onto the back focal plane of a high numericalaperture oil immersion objective (100× UPlanSApo, NA 1.4, Olympus)through the back port of the microscope. A translation stage allowedboth lasers to be shifted towards the edge of the objective so that theemerging light from the objective reached the sample at a high incidentangle near but not exceeding the critical angle of the glass-waterinterface. This excitation scheme allowed fluorophores within a fewmicrometers from the surface to be excited and reduced the backgroundfluorescence from the solution. The fluorescence emission was collectedby the same objective and filtered by a polychroic mirror(z458/514/647rpc, Chroma), a band pass filter (HQ710/70m, Chroma) and along pass filter (HQ665LP, Chroma). The filtered emission was thenimaged onto an EMCCD camera (Ixon DV897DCS-BV, Andor) through a pair ofrelay lenses with a weak cylindrical lens (1 m focal length) inserted inbetween.

To stabilize the microscope focus during data acquisition, the reflectedred excitation laser from the glass-water interface was directed onto aquadrant photodiode by a reflective prism at the back port of themicroscope. The quadrant photodiode read the position of the reflectedlaser, which is sensitive to the distance between the coverglass surfaceand the objective. This information was then fed back to a z-positioningpiezo stage (NanoView-M, MadCity Labs) by software to correct for thez-drift in the microscope focus. This “focus lock” system was capable ofmaintaining the focus position within 40 nm for the duration of STORMdata acquisition. Residual drift in z was corrected during dataanalysis, as described below.

During data acquisition, a relatively strong imaging/deactivation laser(˜40 mW at 657 nm) and a relatively weak activation laser (<2 microwattsat 532 mm) were applied to the sample simultaneously. The simultaneousillumination with both the activation and deactivation lasers resultedin the stochastic switching of the reporter fluorophores between thefluorescent and dark states. A relatively strong imaging/deactivationlaser power was chosen to ensure high emission intensity and a rapidswitching off rate, and the relatively weak activation laser was chosento ensure that the fraction of activated fluorophores at any given timewas sufficiently low so that they were optically resolvable. The EMCCDcamera acquired the images continuously at a frame rate of 20 Hz toobtain a “movie.”

In order to derive the z coordinates from the widths of the singlemolecule images, calibration curves were generated as shown in FIG. 1C.The calibration experiments were performed in Example 1 in threeways: 1. Alexa 647 labeled streptavidin was adsorbed on the coverglasssurface at a low density such that individual streptavidin moleculeswere resolvable from each other. The beta-mercaptoethanol in the imagingbuffer was replaced with 2 mM Trolox so that blinking of the fluorophorewas suppressed. The fluorescence images of individual streptavidinmolecules were recorded while scanning the sample stage in z at aconstant rate with the piezo stage. 2. Quantum dots were adsorbed ontothe coverglass. A solution of 1% beta-mercaptoethanol in PBS was used asthe imaging buffer to suppress the blinking of quantum dots. Thefluorescence images of individual quantum dots were acquired whilescanning the sample stage in z at a constant rate. 3. Cy3-Alexa 647labeled streptavidin was adsorbed on the coverglass surface with highdensity. The measurement was performed in the same way as during dataacquisition except that the sample was scanned slowly in z at a constantrate. Photoactivation events in a small area (usually 8 micrometers×4micrometers) within the view field were used for measuring thecalibration curve. All three measurements produced similar calibrationcurves.

Fluorescent peaks in one image frame of a calibration experiment werefit with an elliptical Gaussian function

${G\left( {x,y} \right)} = {{h\; {\exp \left( {{{- 2}\frac{\left( {x - x_{0}} \right)^{2}}{w_{x}^{2}}} - {2\frac{\left( {y - y_{0}} \right)^{2}}{w_{y}^{2}}}} \right)}} + b}$

where h is the peak height, b is the background, (x₀, y₀) is the centerposition of the peak, and w_(x) and w_(y) stand for the widths of theimage (point spread function, PSF) in the x and y directions,respectively. At the same time, the z position of the correspondingmolecule was determined from the z trajectory of the piezo stage. Thew_(x) and w_(y) values as a function of z were then fit to a modifiedform of a typical defocusing curve:

${w_{x,y}(z)} = {w_{0}\sqrt{1 + \left( \frac{z - c}{d} \right)^{2} + {A\left( \frac{z - c}{d} \right)}^{3} + {B\left( \frac{z - c}{d} \right)}^{4}}}$

where w₀ is the PSF width when a molecule is at the focal plane, c isthe offset of the x or y focal plane from the average focal plane, d isthe focus depth of the microscope, and A and B are coefficients ofhigher order terms to correct for the non-ideality of the imagingoptics. The average focal plane is defined such that a fluorophorepositioned in this plane has an image PSF with equal widths in the x andy directions, thus generating a spherical image. It should be noted thatthese fitting curves were generated to facilitate the automatedz-localization when the measured w_(x) and w_(y) values were comparedwith the calibration curve to search for the corresponding z position.The exact function used for the fitting curve was unimportant as long asthe curves fit the measured calibration data with sufficient precision.

The data were analyzed in a similar manner as described previously (seeInternational Patent Application No. PCT/US2007/017618, filed Aug. 7,2007, entitled “Sub-Diffraction Limit Image Resolution and Other ImagingTechniques,” published as Int. Pat. Apl. Pub. No. WO 2008/091296 on Jul.31, 2008, incorporated herein by reference) but now with the additionalz-dimension information derived from the shape of the image ofindividual activated fluorophores. Fluorescent peaks in each image frameof the STORM movie were identified by fitting local maxima with anelliptical Gaussian function to deduce the peak height h′, the centerposition in the two lateral dimensions, x₀′ and y₀′, and the peak widthsin the two lateral dimensions, w_(x)′ and w_(y)′. Applying a thresholdto the peak height (h′), width (√{square root over (w′_(x)w′_(y))}) andellipticity (w_(x)′/w_(y)′), peaks that were rejected were too weak, toowide or too skewed to yield satisfactory localization accuracy. Alsorejected were certain peaks that would have resulted in overlappingimages of multiple fluorophores. If the center positions of identifiedpeaks in consecutive frames were spatially separated by less than onepixel, they were considered as originating from the same molecule duringone photoactivation event. All images from the same photoactivationevent of the same fluorophore in different frames were averaged and asecond fit to an elliptical Gaussian function was performed to deducethe refined center positions x₀ and y₀, and widths w_(x) and w_(y). Thearea of the image used for the second fit was determined by the peakwidths obtained in the initial fit.

After the second fit, the calibration curve was searched to find a z₀point that best matched the measured widths w_(x) and w_(y) obtainedfrom the fit. This search was performed automatically by minimizing thedistance in the w_(x) ^(1/2)−w_(y) ^(1/2) space:

D=√{square root over ((w _(x) ^(1/2) −w _(x,calib) ^(1/2))²+(w _(y)^(1/2) −w _(y,calib) ^(1/2))²)}

It can be shown by simulation and by an analytical treatment that usingthe square root of the widths improves the accuracy of localization in zin the search procedure as compared to using the widths directly.Activation events with a minimum distance D larger than a presetthreshold indicated that the image was distorted, most likely caused bymore than one molecule located in close proximity and photoactivated inthe same image frame. These events were rejected from further analysis.This procedure allowed the 3D position (x₀, y₀ and z₀) of each activatedfluorophore to be obtained and in this manner the three-dimensionalimage was constructed.

When performing 3D STORM measurements of biological samples in aqueoussolutions supported by glass substrates using an oil immersionobjective, the mismatch of indices of refraction between glass (n=1.515)and the imaging buffer (n=1.35 for 10% glucose solution) may beconsidered. This index of refraction mismatch effectively shifts theapparent z position of an object away from the glass surface. Within afew micrometers from the surface, it was shown that thisrefractive-index-mismatch induced magnification of the z-distance can betreated as a constant and that the magnification factor is equal to 1.26for the objective and refractive indexes used in these imaging condition(objective: NA=1.4, glass: n=1.515 and buffer: n=1.35). This smallmagnification effect was corrected accordingly in the z-localizationanalysis by rescaling all z values, obtained from direct comparison withthe calibration curve, by a factor of 1/1.26=0.79.

Due to aberrations in the imaging optics, the PSF may become asymmetricwhen a fluorophore is out of focus, and as a result, the center of itsimage may deviate slightly from the actual lateral position of thefluorophore. This causes an apparent tilting distortion in the 3D image.The average tilt was typically not more than 4 degrees in theseexperiments and can be corrected by pre-calibration of the tilt profile.

An important factor that affects the localization accuracy is the samplestage drift during the image acquisition time, including both drift inx-y plane and drift in the z direction. In the setup used in Example 1,a focus lock was installed to minimize z-drift, but a residue drift of˜40 nm is present. The drift was corrected using two methods in theseexamples. One method involves adding fiducial markers (fluorescentbeads) to track the drift of the sample and subtracting the movement ofthe markers during image analysis. The other method used the correlationfunction of the image for drift correction. The second method was usedto correct for the x, y and z drift in the above examples. A movie wasdivided in time into equal-period segments and an image was constructedfrom each movie segment. The correlation functions between the image inthe first segment and all subsequent segments were then calculated andthe centroid positions of the correlation functions were determined.Interpolations based on these centroid positions were used to generate acurve of the centroid position as a function of time for each imagingframe. This drift was then subtracted from the localizations and alllocalizations at different time points were included to generate thedrift corrected image.

While several embodiments of the present invention have been describedand illustrated herein, those of ordinary skill in the art will readilyenvision a variety of other means and/or structures for performing thefunctions and/or obtaining the results and/or one or more of theadvantages described herein, and each of such variations and/ormodifications is deemed to be within the scope of the present invention.More generally, those skilled in the art will readily appreciate thatall parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the teachings of thepresent invention is/are used. Those skilled in the art will recognize,or be able to ascertain using no more than routine experimentation, manyequivalents to the specific embodiments of the invention describedherein. It is, therefore, to be understood that the foregoingembodiments are presented by way of example only and that, within thescope of the appended claims and equivalents thereto, the invention maybe practiced otherwise than as specifically described and claimed. Thepresent invention is directed to each individual feature, system,article, material, kit, and/or method described herein. In addition, anycombination of two or more such features, systems, articles, materials,kits, and/or methods, if such features, systems, articles, materials,kits, and/or methods are not mutually inconsistent, is included withinthe scope of the present invention.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

It should also be understood that, unless clearly indicated to thecontrary, in any methods claimed herein that include more than one stepor act, the order of the steps or acts of the method is not necessarilylimited to the order in which the steps or acts of the method arerecited.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

What is claimed is: 1-77. (canceled)
 78. A microscope apparatuscomprising: an illumination system that irradiates light to activate andexcite a fraction of a plurality of entities in a sample; an imagingsystem comprising a non-circularly symmetric lens, wherein the imagingsystem forms a plurality of images of the fraction of the plurality ofentities by fluorescence light emitted from the fraction of theplurality of entities on a detector; and a processor that determines x,y, and z positions of at least some of the plurality of entities in thesample based on the plurality of images, wherein the x, y, and zpositions of the plurality of entities are 3-D spatial coordinates. 79.The microscope apparatus according to claim 78, wherein the processordetermines the z positions of the plurality of entities based on shapesof the plurality of images.
 80. The microscope apparatus according toclaim 79, wherein the processor determines the z positions of theplurality of entities based on shapes of the plurality of ellipsoidalimages.
 81. The microscope apparatus according to claim 78, wherein thelens is a cylindrical lens.
 82. The microscope apparatus according toclaim 78, wherein the processor uses a Gaussian function to determinethe x, y, and z positions.
 83. The microscope apparatus according toclaim 78, wherein the processor uses an elliptical Gaussian function todetermine the x, y, and z positions.
 84. The microscope apparatusaccording to claim 78, wherein the processor calculates the z positionfrom the shape of images within the plurality of images.
 85. Themicroscope apparatus according to claim 78, wherein the processorcalculates the z position from the intensity of images within theplurality of images.
 86. The microscope apparatus according to claim 78,wherein the processor applies drift correction when determining the x,y, and z positions.
 87. The microscope apparatus according to claim 86,wherein applying drift correction comprises using fiducial markers. 88.The microscope apparatus according to claim 86, wherein applying driftcorrection comprises using fluorescent beads.
 89. The microscopeapparatus according to claim 86, wherein applying drift correctioncomprises identifying a fixed point, determining apparent movement ofthe fixed point, and correcting the x, y, and z positions based on theapparent movement of the fixed point.
 90. The microscope apparatusaccording to claim 86, wherein applying the drift correction comprisesusing a correlation function.
 91. The microscope apparatus according toclaim 78, wherein the processor determines x, y, and z positions as afunction of time.
 92. The microscope apparatus according to claim 78,wherein the illumination system irradiates activation light to activatethe fraction of a plurality of entities and excitation light to excitethe fraction of a plurality of entities, wherein the activation lightand the excitation light have substantially the same wavelengths. 93.The microscope apparatus according to claim 78, wherein the illuminationsystem irradiates activation light to activate the fraction of aplurality of entities and excitation light to excite the fraction of aplurality of entities, wherein the activation light and the excitationlight have substantially different wavelengths.
 94. The microscopeapparatus according to claim 78, wherein at least some of the pluralityof entities are separated by a distance of separation less than awavelength of the fluorescence light emitted from the fraction of theplurality of entities.
 95. The microscope apparatus according to claim78, wherein the x, y, and z positions are calculated at a precisionbetter than the diffraction limit of the fluorescence light emitted fromthe fraction of the plurality of entities.
 96. The microscope apparatusaccording to claim 78, wherein at least some of the plurality ofentities comprise cyanine dyes.
 97. The microscope apparatus accordingto claim 78, wherein at least some of the plurality of entitiescomprises fluorescent protein.